No, as it registers immediately with one push.
It doesn't 'speed-up' the waiting time hitting button multiple times!
I do believe that some people take out their 'frustrations' with the poor button, though!

I wonder if many pedestrian crossings require people on both sides to press the button before the lights change, so if I'm the only one, I'll often press it 2, 3 times. especially if I can see a bus or train, but need to cross the road to get to it!

I push twice, that is more than enough, it does not make any difference at all, the lights are programmed. It is annoying to stand next to an impatient person that pushes the button repeatedly! Cant wait two seconds! I also don't touch the button if someone else has already pushed it and the light it lit, no point, lights change when they programmed to...

Pressing the button at lights only lets the control box know that you are there so that you will get the "walk" sign when the lights change. If you don't press the button, you might not get the sign, especially in non-peak hours. Therefore, pressing the button more than once is unnecessary and a bit silly. The lights still have to go through their sequence.

I press it once & wait. There is just no pointing pressing over & over again. It won't make the lights change any faster. Lifts? Once or twice. I seem to be more impatient with a lift, esp' at 1 of the Aldi stores we visit, which has a very slow responding lift to/from the carpark below!